Geometry Without Axioms; Or the First Book of Euclid's Elements. With Alterations and Familiar Notes; and an Intercalary Book in which the Straight Line and Plane are Derived from Properties of the Sphere ...: To which is Added an Appendix ...Robert Heward, 1833 - 150 σελίδες |
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Σελίδα 28
... joins their centres shall pass through the point of contact . For it is one of the points through which the straight line + INTERC.10 . described as by Prop . IX , passes . And there can bet no other straight line between the centres ...
... joins their centres shall pass through the point of contact . For it is one of the points through which the straight line + INTERC.10 . described as by Prop . IX , passes . And there can bet no other straight line between the centres ...
Σελίδα 33
... joining their centres ; + INTERC.10 . the spheres touch + one another externally in the point B. And if Cor . 8. the straight line AC , together with the two substantial spheres Nom . Nom . Cor . whose centres are A and E , be turned ...
... joining their centres ; + INTERC.10 . the spheres touch + one another externally in the point B. And if Cor . 8. the straight line AC , together with the two substantial spheres Nom . Nom . Cor . whose centres are A and E , be turned ...
Σελίδα 38
... join CF , INTERC.12 and let CF bet prolonged to an unlimited length on the side Cor . 6. of L. Let then the spheres BFGH and AFIH be united as one INTERC . 9. body , and together with the straight line CL be turned round the straight ...
... join CF , INTERC.12 and let CF bet prolonged to an unlimited length on the side Cor . 6. of L. Let then the spheres BFGH and AFIH be united as one INTERC . 9. body , and together with the straight line CL be turned round the straight ...
Σελίδα 39
... join AM , BM ; and afterwards let the united spheres be transposed , and turned round BA till M be in the same place ... joins their centres must * pass through M , and it does not ; wherefore they will cut one another in one self ...
... join AM , BM ; and afterwards let the united spheres be transposed , and turned round BA till M be in the same place ... joins their centres must * pass through M , and it does not ; wherefore they will cut one another in one self ...
Σελίδα 40
... join * INTERC.10 . AM , AQ , BM , BQ , and these straight lines will be all equal one to another , because they are radii of the same or equal spheres ; where- Cor . 4 . L G D A M ס N H B sebed A Cor . 1 . fore if about the centres M. 40 ...
... join * INTERC.10 . AM , AQ , BM , BQ , and these straight lines will be all equal one to another , because they are radii of the same or equal spheres ; where- Cor . 4 . L G D A M ס N H B sebed A Cor . 1 . fore if about the centres M. 40 ...
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Geometry Without Axioms; Or the First Book of Euclid's Elements. with ... Thomas Perronet Thompson Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD adjacent angles alternate angles angle ABC angle ACB angle BAC angular points aret assigned point Axiom axis base BC bisected called CEGDHF central distances change of place circle coincide throughout Constr demonstrated double equal angles equal straight lines equal to AC equal to EF equilateral triangle Euclid exterior angle extremities four right angles Geometry given straight line greater hard body inclose a space instance INTERC Intercalary Book ist equal join line AC magnitude manner meet opposite angles parallelogram parity of reasoning pass perpendicular prolonged Prop PROPOSITION proved quadrilateral radii radius rectilinear figure remain unmoved remaining angle remains at rest respectively SCHOLIUM self-rejoining line shown side BC side opposite situation sphere whose centre straight line BC tessera THEOREM.-If third side triangle ABC turned unlimited length Wherefore